Nearest normal-priced supermarket to County Hall

Please could anybody tell me where the nearest normal priced supermarket is to the County Hall.I was directed to a small shop on York Rd??? which was very expensive and did not sell wine!!! I was told that the nearest place to buy a bottle of wine was in Waterloo station.It took me ages - going up and down escalators,pushing through crowds,waiting in queues to eventually get a bottle of wine (not of our choice) and ofcourse double the price of anywhere else.Was I anywhere near a Tesco or similar???!!!!
Also, if anybody else is staying in this area - everybody will direct you to the nearest cash point, as being Waterloo Station(endless queues) - when the nearest is in fact in the Royal Festival Hall - calm and quiet!!!!

Do try Lower Marsh which is only a short walk away from County Hall. There is a good market, especially on weekdays, with some good veg stalls and a large fruit stall. There is also a really good wholefood store, plus Boots, a bakers, but not a butchers.
Supermarkets are a problem, though in my case it is because I hate trying to drag kids round them. Instead we do our main shop around Tatchbrook St in Pimlico. A good market, a brilliant butcher, a lovely cheese shop, a fishmongers, a few good delis and a small Tescos. Vicoria St, which is over the bridge and across Parliament Sq has Sainsburys, plus Army and Navy, and there is an Argos at Victoria.